International Physics Olympiad · Year 2008
Problems
- Problem 1A small particle of mass m starts from rest on a smooth approach track and then enters the inside of a vertical circular loop of radius R at its lowest point. The approach joins the loop smoothly, and the initial height H is measured above the loop bottom. Take g=9.8 m/s² and neglect all friction. (a) Find speed at position angle θ from the upward vertical, taking the bottom as zero potential. (b) Write the normal force and contact condition at the top. (c) Find minimum H to maintain contact throughout, then find the bottom normal force in this limiting case. Use SI units throughout and treat the track and constraints as ideal as specified. State sign conventions, retain units, and check the contact condition at every point of the loop.Solutions: 1
- Problem 2A uniform wire of length L and constant cross-sectional area A has resistivity ρ at fixed temperature. Its ends are connected to an ideal constant-voltage source V; take ρ unchanged by heating, with steady current and no leakage. (a) Find wire resistance R from resistivity. (b) Calculate current I and current density J. (c) Find Joule power P and describe its dependence on L when V,A,ρ are fixed. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.Solutions: 1
- Problem 3Monochromatic light in vacuum has frequency f and wavelength λ. A light photon is described using Planck’s constant h and the speed of light c=3.00×10⁸ m/s; ignore interactions with matter. (a) Relate f and λ through wave propagation. (b) Derive one photon’s energy E_γ in terms of f and then λ. (c) Find momentum magnitude p_γ and check dimensions of E_γ and p_γ. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.Solutions: 1